Chiral formulation for hyperKähler sigma-models on cotangent bundles of symmetric spaces

Abstract

Starting with the projective-superspace off-shell formulation for four-dimensional = 2 supersymmetric sigma-models on cotangent bundles of arbitrary Hermitian symmetric spaces, their on-shell description in terms of = 1 chiral superfields is developed. In particular, we derive a universal representation for the hyperkahler potential in terms of the curvature of the symmetric base space. Within the tangent-bundle formulation for such sigma-models, completed recently in arXiv:0709.2633 and realized in terms of = 1 chiral and complex linear superfields, we give a new universal formula for the superspace Lagrangian. A closed form expression is also derived for the Kahler potential of an arbitrary Hermitian symmetric space in Kahler normal coordinates.